Question

Suppose that y varies directly with x, and y=3 when x=8

(a) Write an inverse equation equation that relates
Equation:

(b) Find y when x=4

Answer 1

we are given

y varies directly with x

so, we can write equation as

`y=kx`

where

k is a constant

now, we need to find k

we are given

y=3 when x=8

so, we can plug it and find k

`3=k*8`

`k=(3)/(8)`

now, we can plug it back

`y=(3)/(8)x`

(A)

we have got equation as

`y=(3)/(8)x`

for finding inverse , we can switch x and y

`x=(3)/(8)y`

now, we can solve for y

`8*x=8*(3)/(8)y`

`8*x=3y`

`f^(-1)(x)=(8x)/(3)`............Answer

(B)

we have

`y=(3)/(8)x`

we can plug x=4 and find y

`y=(3)/(8)*4`

`y=(3)/(2)`................Answer